Answer:
The correct answer is the last option: " Both functions have the same average rate of change over this interval"
Explanation:
If we are given a function h(x), and we want to know the average rate of change in an interval [a, b], we use the formula:
[tex]Average\text{ }rate\text{ }of\text{ }change=\frac{h(a)-h(b)}{a-b}[/tex]In this case, we are looking the interval [0, 1].
In the graph for f(x), we can see:
f(0) = -4
f(1) = 2
The average change of rate of f(x) in [0, 1] is:
[tex]\frac{f(0)-f(1)}{0-1}=\frac{-4-2}{0-1}=\frac{-6}{-1}=6[/tex]In the table for g(x), we can see:
g(0) = 3
g(1) = 9
The average rate of change of g(x) in [0, 1 ] is:
[tex]\frac{g(0)-g(1)}{0-1}=\frac{3-9}{0-1}=\frac{-6}{-1}=6[/tex]Thus, the average rate of change of both functions is the same in [0, 1]